Question

What is the correct inverse function for f(x) = e2x ?

Answer 1

To solve this problem you must appy the proccedure shown below:

1. You have the following function given in the problem above:

f(x)=e^2x

2. You can rewrite is:

y=e^2x

3. Interchange the variables, as below:

x=e^2y

3. The inverse of an exponential function is the logarithm function. Thereforem you have:

ln(x)=ln(e^2y)
ln(x)=2y

4.Then, you have:

y=ln(x)/2

Therefore, the answer is:

f^-1(x)=ln(x)/2